Probing the viscoelastic properties of polyacrylamide polymer gels in a wide frequency range

TL;DR

This study investigates the viscoelastic properties of polyacrylamide gels across a wide frequency spectrum using AFM and rheometry, introducing a fractional derivative model that captures the entire frequency response and reveals physical insights.

Contribution

The paper presents a novel fractional derivative model that accurately describes the viscoelastic behavior of polyacrylamide gels over a broad frequency range, validated by two measurement techniques.

Findings

Perfect agreement between AFM and rheometer data.

Determination of plateau modulus G' and slope nf at low frequencies.

Introduction of a new transition time T and model parameters revealing gel physics.

Abstract

Polymer gels have been shown to behave as viscoelastic materials but only a small amount of data is usually provided in the glassy transition. In this paper, the dynamic moduli G' and G" of polyacrylamide hydrogels are investigated using both an AFM in contact force modulation mode and a classical rheometer. The validity is shown by perfect matching of the two techniques. Measurements are carried out on gels of increasing polymer concentration in a wide frequency range. A model based on fractional derivatives is proposed, covering the whole frequency range. G_0^N, the plateau modulus, as well as nf, the slope of the G" modulus, are obtained at low frequencies. The model also predicts the slope a of both moduli in the transition regime, as well as a new transition time T. The whole frequency spectrum is recovered, and the model parameters contain interesting information about the physics of such gels.